When Big Data Slows Down

Digital Humanities and the Study of Roman Amphitheaters

Sebastian Heath sebastian.heath@nyu.edu

http://commons.wikimedia.org/wiki/File:RomanEmpire_117_recoloured_2.svg

Colosseum

http://commons.wikimedia.org/wiki/File:Colosseum_II.jpg

Amphitheaters around the Empire

Roman Empire Outline: http://awmc.unc.edu/

Pause for Themes, Terms and Questions

Many sizes

RStudio

http://www.r-project.org & http://rstudio.org

Media Rich (Google)

Assisi in Italy (Maximum dimension not known? Arena 65 x 38 Meters)

Media Rich (Google)

Carsulae in Italy (84 x 62 Meters)

Gladiators, Beast Hunts and Executions

The Zliten (Libya) Mosaic (C. 2nd Century AD?)

http://upload.wikimedia.org/wikipedia/commons/8/8d/Bestiarii.jpg

http://upload.wikimedia.org/wikipedia/commons/thumb/3/32/Circus_Leptis_Magna_Libya.JPG/1024px-Circus_Leptis_Magna_Libya.JPG

Many sizes… but not all shapes

“Media Rich” (Nimes)

http://commons.wikimedia.org/wiki/File:Arena_of_Nimes_2_HDR.jpg

“Media Rich” (Nimes)

“Media Rich” (Trier)

Public Information

http://www.maumburyrings.co.uk or “Peak Amphitheater”

How many amphitheater seats were there?

ramphs.all <- ramphs
ramphs.all.sp <- ramphs.sp

ramphs <- ramphs[ramphs$include,]
ramphs.sp <- ramphs.sp[ramphs.sp$include,]
  
ramphs$imputed.capacity <- NA
ramphs$imputed.capacity[!(is.na(ramphs$capacity))] <- ramphs[!(is.na(ramphs$capacity)),]$capacity

lm.imp.1 <- lm ( capacity ~ latitude +
                   ext.major + ext.minor + arena.major +
                   arena.minor + arena.major:ext.minor + arena.minor * ext.minor,
                data=ramphs )

pred.1 <- predict (lm.imp.1, ramphs)
ramphs$imputed.capacity <- ifelse (is.na(ramphs$capacity), pred.1, ramphs$capacity)

lm(capacity ~ ext.major, ramphs[(ramphs$ext.major < 120) & (ramphs$ext.major > 50),]) -> lm.ext.major
ramphs$imputed.capacity[(!is.na(ramphs$ext.major)) & (is.na(ramphs$imputed.capacity))] <- ramphs$ext.major[(!is.na(ramphs$ext.major)) & (is.na(ramphs$imputed.capacity))] * lm.ext.major$coefficients[2]

length(ramphs$imputed.capacity[is.na(ramphs$imputed.capacity)])
## [1] 76
ramphs$imputed.capacity[is.na(ramphs$imputed.capacity)] <- 5000

sum(ramphs$imputed.capacity)
## [1] 2287222

With many thanks to Katie Anderson of NYU Libaries Data Services who is in no way responsible for my (mis?)use of her work.

Where are the amphitheaters seats?

Spatial History

R. White. What is Spatial History? Spatial History Lab: Working paper; Submitted 1 February 2010;

Paragraph 36 (emphasis author): “One of the important points that I want to make about visualizations, spatial relations, and spatial history is something that I did not fully understand until I started doing this work and which I have had a hard time communicating fully to my colleagues: visualization and spatial history are not about producing illustrations or maps to communicate things that you have discovered by other means. It is a means of doing research; it generates questions that might otherwise go unasked, it reveals historical relations that might otherwise go unnoticed, and it undermines, or substantiates, stories upon which we build our own versions of the past.”

Calculating Distances

Who should know how to do this?

#generate distances of all amphitheaters to all other amphitheaters
ramphs.dists <- spDists(ramphs.sp,ramphs.sp,longlat = TRUE)

# but let's use names
colnames(ramphs.dists) <- ramphs$id
rownames(ramphs.dists) <- ramphs$id

# Would be nice to have a d.f in the form from,to,km
as.data.frame(ramphs.dists) -> ramphs.dists.df

#add column of names, in anticipation of using gather()
cbind(from = ramphs$id,ramphs.dists.df) -> ramphs.dists.df

gather(ramphs.dists.df, to, km, 2:dim(ramphs.dists.df)[2]) -> ramphs.dists.df

# data now in nice columns but...
# we still have the 0Km rows.
#set phasers to kill...
ramphs.dists.df[ramphs.dists.df$km > 0,] -> ramphs.dists.df

The Data

from to km
2 arlesAmphitheater duraEuroposAmphitheater 3241.8637
3 lyonAmphitheater duraEuroposAmphitheater 3255.7344
4 ludusMagnusArena duraEuroposAmphitheater 2579.2087
5 romeFlavianAmphitheater duraEuroposAmphitheater 2579.4293
6 romeAmphitheatrumCastrense duraEuroposAmphitheater 2577.5114
7 eleutheropolisAmphitheater duraEuroposAmphitheater 645.7789
8 meridaAmphitheater duraEuroposAmphitheater 4177.5360
9 newsteadAmphitheater duraEuroposAmphitheater 4025.3811
10 conimbrigaAmphitheater duraEuroposAmphitheater 4341.4319
11 cumaeAmphitheater duraEuroposAmphitheater 2433.6452
12 pozzuoliFlavianAmphitheater duraEuroposAmphitheater 2427.6184
13 pozzuoliEarlyAmphitheater duraEuroposAmphitheater 2427.4305
14 syracuseAmphitheater duraEuroposAmphitheater 2304.6697
15 carthageAmphitheater duraEuroposAmphitheater 2747.3387
16 hadrianVillaAmphitheater duraEuroposAmphitheater 2556.7911
17 corinthAmphitheater duraEuroposAmphitheater 1636.6076
18 marcianopolisAmphitheater duraEuroposAmphitheater 1474.9250
19 porolissumAmphitheater duraEuroposAmphitheater 2013.5727
20 nijmegenAmphitheater duraEuroposAmphitheater 3355.6355
21 carnuntumMilitaryAmphitheater duraEuroposAmphitheater 2466.9678
22 carnuntumLudus duraEuroposAmphitheater 2468.9590
23 carnuntumCivilianAmphitheater duraEuroposAmphitheater 2468.8220
24 leptisMagnaAmphitheater duraEuroposAmphitheater 2453.6977
25 empuriesAmphitheater duraEuroposAmphitheater 3355.0218
26 tarragonaAmphitheater duraEuroposAmphitheater 3509.8708
27 cagliariAmphitheater duraEuroposAmphitheater 2843.1324
28 italicaAmphitheater duraEuroposAmphitheater 4179.6454
29 segobrigaAmphitheater duraEuroposAmphitheater 3862.8982
30 catiniaAmphitheater duraEuroposAmphitheater 2321.2086
31 paestumAmphitheater duraEuroposAmphitheater 2347.9264
32 lunaAmphitheater duraEuroposAmphitheater 2818.9115
33 casinumAmphitheater duraEuroposAmphitheater 2463.0371
34 viminaciumAmphitheater duraEuroposAmphitheater 1997.6238
35 flaviaSolvaAmphitheater duraEuroposAmphitheater 2491.4773
36 rusellaeAmphitheater duraEuroposAmphitheater 2704.1570
37 parisAmphitheater duraEuroposAmphitheater 3503.1993
38 octodurusForumClaudiiVallensiumAmphitheater duraEuroposAmphitheater 3091.3570
39 cyreneAmphitheater duraEuroposAmphitheater 1758.7145
40 libarnaAmphitheater duraEuroposAmphitheater 2922.8465
41 luceriaNoukeriaAmphitheater duraEuroposAmphitheater 2338.2406
42 avellaAmphitheater duraEuroposAmphitheater 2389.3544
43 nimesAmphitheater duraEuroposAmphitheater 3265.2724
44 charterhouseAmphitheater duraEuroposAmphitheater 3913.4313
45 chesterAmphitheater duraEuroposAmphitheater 3968.2666
46 gennesAmphitheater duraEuroposAmphitheater 3665.4275
47 scylletiumScolaciumAmphitheater duraEuroposAmphitheater 2194.2565
48 oudnaAmphitheater duraEuroposAmphitheater 2762.5166
49 carthagoNovaAmphitheater duraEuroposAmphitheater 3734.8512
50 virunumAmphitheater duraEuroposAmphitheater 2573.2558
51 carsulaeAmphitheater duraEuroposAmphitheater 2587.5644
52 florenceAmphitheater duraEuroposAmphitheater 2715.0934
53 ocriculumAmphitheater duraEuroposAmphitheater 2590.6507
54 lixusAmphitheater duraEuroposAmphitheater 4236.4306
55 arezzoAmphitheater duraEuroposAmphitheater 2659.1569
56 larinumAmphitheater duraEuroposAmphitheater 2379.4143
57 lucusFeroniaeAmphitheater duraEuroposAmphitheater 2575.1280
58 allifaeAmphitheater duraEuroposAmphitheater 2418.0908
59 cimiezAmphitheater duraEuroposAmphitheater 3030.6213
60 hydataHypsitanaForumTraianiAmphitheatre duraEuroposAmphitheater 2870.7728
61 luccaAmphitheater duraEuroposAmphitheater 2776.2445
62 hispellumAmphitheatre duraEuroposAmphitheater 2586.4036
63 veronaAmphitheatre duraEuroposAmphitheater 2777.8239
64 aquincumCivilAmphitheater duraEuroposAmphitheater 2295.8815
65 aquincumMilitaryAmphitheater duraEuroposAmphitheater 2294.5178
66 aldburoughAmphitheater duraEuroposAmphitheater 3897.0494
67 perigueuxAmphitheatre duraEuroposAmphitheater 3567.3616
68 cividateCamunoAmphitheater duraEuroposAmphitheater 2845.9662
69 grumentoAmphitheater duraEuroposAmphitheater 2269.7408
70 albaFucensAmphitheater duraEuroposAmphitheater 2507.4774
71 colAugustaRauricaAmphitheatre duraEuroposAmphitheater 3080.9122
72 sutriumAmphitheatre duraEuroposAmphitheater 2606.8748
73 sarmizegetusaAmphitheatre duraEuroposAmphitheater 1932.7637
74 salonaAmphitheatre duraEuroposAmphitheater 2300.9942
75 londonAmphitheatre duraEuroposAmphitheater 3739.6890
76 tiburAmphitheater duraEuroposAmphitheater 2555.5455
77 caerleonAmphitheater duraEuroposAmphitheater 3935.9530
78 telesiaAmphitheatre duraEuroposAmphitheater 2402.6495
79 urbisagliaAmphitheater duraEuroposAmphitheater 2533.6269
80 saintesAmphitheatre duraEuroposAmphitheater 3678.1577
81 assisiAmphitheatre duraEuroposAmphitheater 2591.6974
82 durresAmphitheatre duraEuroposAmphitheater 1998.7495
83 lambaesisAmphitheater duraEuroposAmphitheater 3127.0012
84 mactarisAmphitheater duraEuroposAmphitheater 2857.1786
85 cirencesterAmphitheater duraEuroposAmphitheater 3871.4994
86 vindonissaAmphitheater duraEuroposAmphitheater 3043.5466
87 thysdrusSmallAmphitheater duraEuroposAmphitheater 2730.0252
88 frejusAmphitheater duraEuroposAmphitheater 3070.4752
89 gortynAmphitheater duraEuroposAmphitheater 1440.7413
90 leptiminusAmphitheater duraEuroposAmphitheater 2710.4584
91 miciaAmphitheater duraEuroposAmphitheater 1954.3939
92 gemellaeAmphitheater duraEuroposAmphitheater 3209.0205
93 cherchellAmphitheater duraEuroposAmphitheater 3470.7413
94 pulaAmphitheater duraEuroposAmphitheater 2544.6444
95 carmonaAmphitheater duraEuroposAmphitheater 4144.6798
96 caesareaAmphitheater duraEuroposAmphitheater 595.2877
97 pergamumAmphitheater duraEuroposAmphitheater 1299.6263
98 anazarbusAmphitheater duraEuroposAmphitheater 516.0525
99 antiochAmphitheater duraEuroposAmphitheater 444.7205
100 cyzicusAmphitheater duraEuroposAmphitheater 1294.0974
101 sabrathaAmphitheater duraEuroposAmphitheater 2615.5671

Amphitheaters Closer <= 80 Km.

from to km
258 nimesAmphitheater arlesAmphitheater 27.9687539
650 romeFlavianAmphitheater ludusMagnusArena 0.2207755
651 romeAmphitheatrumCastrense ludusMagnusArena 1.6972845
661 hadrianVillaAmphitheater ludusMagnusArena 24.2518151
698 ocriculumAmphitheater ludusMagnusArena 57.9313847
702 lucusFeroniaeAmphitheater ludusMagnusArena 27.8779458
715 albaFucensAmphitheater ludusMagnusArena 78.8128462
717 sutriumAmphitheatre ludusMagnusArena 44.5686800
721 tiburAmphitheater ludusMagnusArena 26.3424522
775 monteleoneAmphitheater ludusMagnusArena 48.6032488
828 genzanoPrivateAmphitheater ludusMagnusArena 27.5479283
841 portusOvalStructure ludusMagnusArena 23.0421650
843 statiliusTaurusAmphitheater ludusMagnusArena 2.3386907
851 faleriiNoviAmphitheater ludusMagnusArena 47.1219778
864 ludusMagnusArena romeFlavianAmphitheater 0.2207755
866 romeAmphitheatrumCastrense romeFlavianAmphitheater 1.9179319
876 hadrianVillaAmphitheater romeFlavianAmphitheater 24.4592422
913 ocriculumAmphitheater romeFlavianAmphitheater 57.8988659
917 lucusFeroniaeAmphitheater romeFlavianAmphitheater 27.9206250
930 albaFucensAmphitheater romeFlavianAmphitheater 79.0177124
932 sutriumAmphitheatre romeFlavianAmphitheater 44.4399399
936 tiburAmphitheater romeFlavianAmphitheater 26.5447118
990 monteleoneAmphitheater romeFlavianAmphitheater 48.7236605
1043 genzanoPrivateAmphitheater romeFlavianAmphitheater 27.7012943
1056 portusOvalStructure romeFlavianAmphitheater 22.8677014
1058 statiliusTaurusAmphitheater romeFlavianAmphitheater 2.1340177
1066 faleriiNoviAmphitheater romeFlavianAmphitheater 47.0474041
1079 ludusMagnusArena romeAmphitheatrumCastrense 1.6972845
1080 romeFlavianAmphitheater romeAmphitheatrumCastrense 1.9179319
1091 hadrianVillaAmphitheater romeAmphitheatrumCastrense 22.6892929
1128 ocriculumAmphitheater romeAmphitheatrumCastrense 58.2690286
1132 lucusFeroniaeAmphitheater romeAmphitheatrumCastrense 27.6677326
1145 albaFucensAmphitheater romeAmphitheatrumCastrense 77.2652498
1147 sutriumAmphitheatre romeAmphitheatrumCastrense 45.6300686
1151 tiburAmphitheater romeAmphitheatrumCastrense 24.8254037
1205 monteleoneAmphitheater romeAmphitheatrumCastrense 47.7546597
1258 genzanoPrivateAmphitheater romeAmphitheatrumCastrense 26.3553070
1271 portusOvalStructure romeAmphitheatrumCastrense 24.3721923
1273 statiliusTaurusAmphitheater romeAmphitheatrumCastrense 3.9825622
1281 faleriiNoviAmphitheater romeAmphitheatrumCastrense 47.7821715
2096 bobadelaAmphitheater conimbrigaAmphitheater 58.7178710
2162 pozzuoliFlavianAmphitheater cumaeAmphitheater 6.1073447
2163 pozzuoliEarlyAmphitheater cumaeAmphitheater 6.2837252
2183 casinumAmphitheater cumaeAmphitheater 73.7562075
2192 avellaAmphitheater cumaeAmphitheater 48.4031736
2208 allifaeAmphitheater cumaeAmphitheater 58.5692162
2228 telesiaAmphitheatre cumaeAmphitheater 56.5159704
2284 beneventoAmphitheater cumaeAmphitheater 68.9187382
2285 calviRisortaAmphitheater cumaeAmphitheater 40.5962748
2296 capuaRepublicanAmphitheater cumaeAmphitheater 31.5102458
2297 capuaImperialAmphitheater cumaeAmphitheater 31.6279460
2298 liternoAmphitheater cumaeAmphitheater 9.0374043
2299 noleAmphitheater cumaeAmphitheater 40.2940775
2310 noceraSuperioreAmphitheater cumaeAmphitheater 51.8324988
2325 aquinoAmphitheater cumaeAmphitheater 78.6335590
2364 minturnaeAmphitheater cumaeAmphitheater 50.7130994
2365 sinuessaAmphitheater cumaeAmphitheater 38.8242914
2376 cumaeAmphitheater pozzuoliFlavianAmphitheater 6.1073447
2378 pozzuoliEarlyAmphitheater pozzuoliFlavianAmphitheater 0.1970432
2398 casinumAmphitheater pozzuoliFlavianAmphitheater 77.1704472
2407 avellaAmphitheater pozzuoliFlavianAmphitheater 43.4014628
2423 allifaeAmphitheater pozzuoliFlavianAmphitheater 58.1718231
2443 telesiaAmphitheatre pozzuoliFlavianAmphitheater 54.2711716
2499 beneventoAmphitheater pozzuoliFlavianAmphitheater 64.7172784
2500 calviRisortaAmphitheater pozzuoliFlavianAmphitheater 41.7859029
2511 capuaRepublicanAmphitheater pozzuoliFlavianAmphitheater 30.5667414
2512 capuaImperialAmphitheater pozzuoliFlavianAmphitheater 30.7001985
2513 liternoAmphitheater pozzuoliFlavianAmphitheater 13.2343994
2514 noleAmphitheater pozzuoliFlavianAmphitheater 35.1755547
2525 noceraSuperioreAmphitheater pozzuoliFlavianAmphitheater 45.7526823
2579 minturnaeAmphitheater pozzuoliFlavianAmphitheater 55.2462354
2580 sinuessaAmphitheater pozzuoliFlavianAmphitheater 43.2720751
2591 cumaeAmphitheater pozzuoliEarlyAmphitheater 6.2837252
2592 pozzuoliFlavianAmphitheater pozzuoliEarlyAmphitheater 0.1970432
2613 casinumAmphitheater pozzuoliEarlyAmphitheater 77.2015414
2622 avellaAmphitheater pozzuoliEarlyAmphitheater 43.2076626
2638 allifaeAmphitheater pozzuoliEarlyAmphitheater 58.0807452
2658 telesiaAmphitheatre pozzuoliEarlyAmphitheater 54.1308566
2714 beneventoAmphitheater pozzuoliEarlyAmphitheater 64.5340894
2715 calviRisortaAmphitheater pozzuoliEarlyAmphitheater 41.7470277
2726 capuaRepublicanAmphitheater pozzuoliEarlyAmphitheater 30.4682517
2727 capuaImperialAmphitheater pozzuoliEarlyAmphitheater 30.6020895
2728 liternoAmphitheater pozzuoliEarlyAmphitheater 13.3253543
2729 noleAmphitheater pozzuoliEarlyAmphitheater 34.9808437
2740 noceraSuperioreAmphitheater pozzuoliEarlyAmphitheater 45.5688926
2794 minturnaeAmphitheater pozzuoliEarlyAmphitheater 55.3241795
2795 sinuessaAmphitheater pozzuoliEarlyAmphitheater 43.3485126
2825 catiniaAmphitheater syracuseAmphitheater 50.9785638
3058 oudnaAmphitheater carthageAmphitheater 30.3648270
3195 uticaAmphitheater carthageAmphitheater 31.6378238
3196 tebourbaAmphitheater carthageAmphitheater 42.8836577
3197 hencherElKasbatAmphitheater carthageAmphitheater 62.5833037
3203 pupputAmphitheater carthageAmphitheater 55.9193622
3212 carpisAmphitheater carthageAmphitheater 24.1028949
3229 ludusMagnusArena hadrianVillaAmphitheater 24.2518151
3230 romeFlavianAmphitheater hadrianVillaAmphitheater 24.4592422
3231 romeAmphitheatrumCastrense hadrianVillaAmphitheater 22.6892929
3276 carsulaeAmphitheater hadrianVillaAmphitheater 79.5150391
3278 ocriculumAmphitheater hadrianVillaAmphitheater 58.1566593
3282 lucusFeroniaeAmphitheater hadrianVillaAmphitheater 25.8478135

As a Network

Bigger Labels

Degree

http://www.slideshare.net/gcheliotis/social-network-analysis-3273045

##    Min. 1st Qu.  Median    Mean 3rd Qu.    Max. 
##    1.00    1.00    3.00    6.55   10.50   22.00

High Degree

# print the top quartile
V(close.amphitheaters.nw)[degree >= summary(V(close.amphitheaters.nw)$degree/2)[5]]
## Vertex sequence:
##  [1] "ludusMagnusArena"                 "romeFlavianAmphitheater"         
##  [3] "romeAmphitheatrumCastrense"       "cumaeAmphitheater"               
##  [5] "pozzuoliFlavianAmphitheater"      "pozzuoliEarlyAmphitheater"       
##  [7] "carthageAmphitheater"             "hadrianVillaAmphitheater"        
##  [9] "paestumAmphitheater"              "casinumAmphitheater"             
## [11] "luceriaNoukeriaAmphitheater"      "avellaAmphitheater"              
## [13] "oudnaAmphitheater"                "carsulaeAmphitheater"            
## [15] "ocriculumAmphitheater"            "arezzoAmphitheater"              
## [17] "larinumAmphitheater"              "lucusFeroniaeAmphitheater"       
## [19] "allifaeAmphitheater"              "hispellumAmphitheatre"           
## [21] "albaFucensAmphitheater"           "sutriumAmphitheatre"             
## [23] "tiburAmphitheater"                "telesiaAmphitheatre"             
## [25] "urbisagliaAmphitheater"           "assisiAmphitheatre"              
## [27] "mactarisAmphitheater"             "thysdrusSmallAmphitheater"       
## [29] "leptiminusAmphitheater"           "bararusAmphitheater"             
## [31] "sanBenedettoDeiMarsiAmphitheater" "monteleoneAmphitheater"          
## [33] "bolsenaAmphitheater"              "ascoliPicenoAmphitheater"        
## [35] "beneventoAmphitheater"            "calviRisortaAmphitheater"        
## [37] "sanVittorinoAmphitheater"         "capuaRepublicanAmphitheater"     
## [39] "capuaImperialAmphitheater"        "liternoAmphitheater"             
## [41] "noleAmphitheater"                 "noceraSuperioreAmphitheater"     
## [43] "aquinoAmphitheater"               "seressiAmphitheater"             
## [45] "chemtouAmphitheater"              "bekaltaAmphitheater"             
## [47] "sidiBouArkoubAmphitheater"        "genzanoPrivateAmphitheater"      
## [49] "ainHedjahAmphitheater"            "uticaAmphitheater"               
## [51] "tebourbaAmphitheater"             "hencherElKasbatAmphitheater"     
## [53] "hencherZembraAmphitheater"        "bullaRegiaAmphitheater"          
## [55] "pupputAmphitheater"               "siccaVeneriaAmphitheater"        
## [57] "thibariAmphitheater"              "portusOvalStructure"             
## [59] "statiliusTaurusAmphitheater"      "carpisAmphitheater"              
## [61] "faleriiNoviAmphitheater"          "teramoAmphitheater"              
## [63] "ordonaAmphitheater"               "bevanaAmphitheater"              
## [65] "minturnaeAmphitheater"            "sinuessaAmphitheater"

Mapping Degree

Plotting Degree

Distance to Road

http://darmc.harvard.edu/

Counting Seats Near Roads

Seats Near “Major” Cities

… and Riots

alt text http://upload.wikimedia.org/wikipedia/commons/0/03/Pompeian_mural_depicting_the_Amphitheatre_riots.jpg

Blatant Eye Candy?